Open AccessA Stepwise Approach for High-Dimensional Gaussian Graphical Models
Author(s) -
Ruben H. Zamar,
Marcelo Ruíz,
Ginette Lafit,
Javier Nogales
Publication year - 2021
Publication title -
journal of data science, statistics, and visualisation
Language(s) - English
Resource type - Journals
ISSN - 2773-0689
DOI - 10.52933/jdssv.v1i2.11
Subject(s) - graphical model , partial correlation , gaussian , correlation , stepwise regression , lasso (programming language) , computer science , algorithm , graph , relation (database) , minification , exploit , canonical correlation , mathematics , mathematical optimization , artificial intelligence , data mining , machine learning , theoretical computer science , physics , geometry , computer security , quantum mechanics , world wide web
We present a stepwise approach to estimate high dimensional Gaussian graphical models. We exploit the relation between the partial correlation coefficients and the distribution of the prediction errors, and parametrize the model in terms of the Pearson correlation coefficients between the prediction errors of the nodes’ best linear predictors. We propose a novel stepwise algorithm for detecting pairs of conditionally dependent variables. We compare the proposed algorithm with existing methods including graphical lasso (Glasso), constrained `l1-minimization(CLIME) and equivalent partial correlation (EPC), via simulation studies and real life applications. In our simulation study we consider several model settings and report the results using different performance measures that look at desirable features of the recovered graph.